LMFDB - Embedded newform 112.6.i.g.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,6,Mod(65,112)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("112.65");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	112.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.9629878191$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3 x^{9} - 119 x^{8} - 521 x^{7} - 898 x^{6} + 27806 x^{5} + 657990 x^{4} + 3648839 x^{3} + \cdots + 92895579 $ x^10 - 3x^9 - 119x^8 - 521x^7 - 898x^6 + 27806x^5 + 657990x^4 + 3648839x^3 + 1863790x^2 - 25332057*x + 92895579
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{18}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			65.3
Root			$11.5439 + 0.371202i$ of defining polynomial
Character	$\chi$	$=$	112.65
Dual form			112.6.i.g.81.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.11280 + 5.39153i) q^{3} +(-4.70275 + 8.14541i) q^{5} +(-105.969 - 74.6834i) q^{7} +(102.121 - 176.879i) q^{9} +O(q^{10})$	\(q+(3.11280 + 5.39153i) q^{3} +(-4.70275 + 8.14541i) q^{5} +(-105.969 - 74.6834i) q^{7} +(102.121 - 176.879i) q^{9} +(382.558 + 662.609i) q^{11} +732.172 q^{13} -58.5549 q^{15} +(-241.290 - 417.927i) q^{17} +(-1308.54 + 2266.45i) q^{19} +(72.7976 - 803.808i) q^{21} +(-267.753 + 463.762i) q^{23} +(1518.27 + 2629.72i) q^{25} +2784.35 q^{27} +3943.87 q^{29} +(1831.72 + 3172.64i) q^{31} +(-2381.65 + 4125.14i) q^{33} +(1106.67 - 511.942i) q^{35} +(-6319.51 + 10945.7i) q^{37} +(2279.11 + 3947.53i) q^{39} +4814.47 q^{41} +4938.11 q^{43} +(960.499 + 1663.63i) q^{45} +(8702.49 - 15073.2i) q^{47} +(5651.79 + 15828.2i) q^{49} +(1502.18 - 2601.85i) q^{51} +(2329.22 + 4034.32i) q^{53} -7196.30 q^{55} -16292.8 q^{57} +(16250.4 + 28146.6i) q^{59} +(21748.1 - 37668.8i) q^{61} +(-24031.5 + 11116.9i) q^{63} +(-3443.23 + 5963.84i) q^{65} +(-16041.2 - 27784.1i) q^{67} -3333.85 q^{69} -15820.0 q^{71} +(-18257.7 - 31623.3i) q^{73} +(-9452.13 + 16371.6i) q^{75} +(8946.70 - 98786.6i) q^{77} +(12736.1 - 22059.5i) q^{79} +(-16148.3 - 27969.6i) q^{81} -69443.5 q^{83} +4538.91 q^{85} +(12276.5 + 21263.5i) q^{87} +(-54165.4 + 93817.2i) q^{89} +(-77587.5 - 54681.1i) q^{91} +(-11403.6 + 19751.6i) q^{93} +(-12307.4 - 21317.1i) q^{95} +94569.1 q^{97} +156269. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 13 q^{3} - 31 q^{5} + 92 q^{7} - 230 q^{9}+O(q^{10}) $ 10 * q + 13 * q^3 - 31 * q^5 + 92 * q^7 - 230 * q^9	$ 10 q + 13 q^{3} - 31 q^{5} + 92 q^{7} - 230 q^{9} - 351 q^{11} - 108 q^{13} - 1214 q^{15} - 111 q^{17} + 1035 q^{19} - 1365 q^{21} + 3639 q^{23} - 1540 q^{25} - 7214 q^{27} - 1468 q^{29} + 7677 q^{31} + 7439 q^{33} - 19899 q^{35} - 13595 q^{37} - 1406 q^{39} + 10620 q^{41} - 1528 q^{43} - 38978 q^{45} + 6675 q^{47} + 30122 q^{49} + 20975 q^{51} + 30753 q^{53} - 56534 q^{55} - 28778 q^{57} + 87989 q^{59} - 19899 q^{61} - 147318 q^{63} - 119470 q^{65} - 33067 q^{67} + 200798 q^{69} + 217440 q^{71} - 141659 q^{73} + 108788 q^{75} + 271471 q^{77} + 118919 q^{79} + 143851 q^{81} - 422008 q^{83} - 286758 q^{85} + 302154 q^{87} + 55861 q^{89} - 403912 q^{91} - 410381 q^{93} - 26279 q^{95} + 270940 q^{97} + 600308 q^{99}+O(q^{100}) $ 10 * q + 13 * q^3 - 31 * q^5 + 92 * q^7 - 230 * q^9 - 351 * q^11 - 108 * q^13 - 1214 * q^15 - 111 * q^17 + 1035 * q^19 - 1365 * q^21 + 3639 * q^23 - 1540 * q^25 - 7214 * q^27 - 1468 * q^29 + 7677 * q^31 + 7439 * q^33 - 19899 * q^35 - 13595 * q^37 - 1406 * q^39 + 10620 * q^41 - 1528 * q^43 - 38978 * q^45 + 6675 * q^47 + 30122 * q^49 + 20975 * q^51 + 30753 * q^53 - 56534 * q^55 - 28778 * q^57 + 87989 * q^59 - 19899 * q^61 - 147318 * q^63 - 119470 * q^65 - 33067 * q^67 + 200798 * q^69 + 217440 * q^71 - 141659 * q^73 + 108788 * q^75 + 271471 * q^77 + 118919 * q^79 + 143851 * q^81 - 422008 * q^83 - 286758 * q^85 + 302154 * q^87 + 55861 * q^89 - 403912 * q^91 - 410381 * q^93 - 26279 * q^95 + 270940 * q^97 + 600308 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	3.11280	+	5.39153i	0.199686	+	0.345867i	0.948427	−	0.316997i	$-0.102674\pi$
$3$	3.11280	+	5.39153i	0.199686	+	0.345867i	−0.748740	+	0.662863i	$0.769341\pi$
$4$		0			0
$5$	−4.70275	+	8.14541i	−0.0841254	+	0.145709i	−0.905018	−	0.425373i	$-0.860143\pi$
$5$	−4.70275	+	8.14541i	−0.0841254	+	0.145709i	0.820893	+	0.571082i	$0.193476\pi$
$6$		0			0
$7$	−105.969	−	74.6834i	−0.817397	−	0.576075i
$7$	−105.969	−	74.6834i	−0.817397	−	0.576075i
$8$		0			0
$9$	102.121	−	176.879i	0.420251	−	0.727896i
$10$		0			0
$11$	382.558	+	662.609i	0.953269	+	1.65111i	0.738282	+	0.674493i	$0.235638\pi$
$11$	382.558	+	662.609i	0.953269	+	1.65111i	0.214987	+	0.976617i	$0.431029\pi$
$12$		0			0
$13$	732.172			1.20159			0.600793	−	0.799405i	$-0.294852\pi$
$13$	732.172			1.20159			0.600793	+	0.799405i	$0.294852\pi$
$14$		0			0
$15$	−58.5549			−0.0671947
$16$		0			0
$17$	−241.290	−	417.927i	−0.202496	−	0.350734i	0.746836	−	0.665009i	$-0.231572\pi$
$17$	−241.290	−	417.927i	−0.202496	−	0.350734i	−0.949332	+	0.314274i	$0.898239\pi$
$18$		0			0
$19$	−1308.54	+	2266.45i	−0.831576	+	1.44033i	0.0652125	+	0.997871i	$0.479227\pi$
$19$	−1308.54	+	2266.45i	−0.831576	+	1.44033i	−0.896788	+	0.442460i	$0.854106\pi$
$20$		0			0
$21$	72.7976	−	803.808i	0.0360221	−	0.397745i
$22$		0			0
$23$	−267.753	+	463.762i	−0.105539	+	0.182800i	−0.913958	−	0.405808i	$-0.866990\pi$
$23$	−267.753	+	463.762i	−0.105539	+	0.182800i	0.808419	+	0.588607i	$0.200324\pi$
$24$		0			0
$25$	1518.27	+	2629.72i	0.485846	+	0.841510i
$26$		0			0
$27$	2784.35			0.735046
$28$		0			0
$29$	3943.87			0.870819			0.435409	−	0.900233i	$-0.356604\pi$
$29$	3943.87			0.870819			0.435409	+	0.900233i	$0.356604\pi$
$30$		0			0
$31$	1831.72	+	3172.64i	0.342338	+	0.592947i	0.984866	−	0.173315i	$-0.0554478\pi$
$31$	1831.72	+	3172.64i	0.342338	+	0.592947i	−0.642528	+	0.766262i	$0.722114\pi$
$32$		0			0
$33$	−2381.65	+	4125.14i	−0.380709	+	0.659408i
$34$		0			0
$35$	1106.67	−	511.942i	0.152703	−	0.0706400i
$36$		0			0
$37$	−6319.51	+	10945.7i	−0.758890	+	1.31444i	0.184527	+	0.982827i	$0.440925\pi$
$37$	−6319.51	+	10945.7i	−0.758890	+	1.31444i	−0.943417	+	0.331609i	$0.892409\pi$
$38$		0			0
$39$	2279.11	+	3947.53i	0.239940	+	0.415589i
$40$		0			0
$41$	4814.47			0.447290			0.223645	−	0.974671i	$-0.428204\pi$
$41$	4814.47			0.447290			0.223645	+	0.974671i	$0.428204\pi$
$42$		0			0
$43$	4938.11			0.407277			0.203638	−	0.979046i	$-0.434723\pi$
$43$	4938.11			0.407277			0.203638	+	0.979046i	$0.434723\pi$
$44$		0			0
$45$	960.499	+	1663.63i	0.0707076	+	0.122469i
$46$		0			0
$47$	8702.49	−	15073.2i	0.574644	−	0.995312i	−0.421436	−	0.906858i	$-0.638474\pi$
$47$	8702.49	−	15073.2i	0.574644	−	0.995312i	0.996080	−	0.0884544i	$-0.0281928\pi$
$48$		0			0
$49$	5651.79	+	15828.2i	0.336276	+	0.941763i
$50$		0			0
$51$	1502.18	−	2601.85i	0.0808715	−	0.140074i
$52$		0			0
$53$	2329.22	+	4034.32i	0.113899	+	0.197279i	0.917339	−	0.398107i	$-0.130333\pi$
$53$	2329.22	+	4034.32i	0.113899	+	0.197279i	−0.803440	+	0.595386i	$0.796999\pi$
$54$		0			0
$55$	−7196.30			−0.320776
$56$		0			0
$57$	−16292.8			−0.664217
$58$		0			0
$59$	16250.4	+	28146.6i	0.607763	+	1.05268i	0.991608	+	0.129280i	$0.0412665\pi$
$59$	16250.4	+	28146.6i	0.607763	+	1.05268i	−0.383845	+	0.923398i	$0.625400\pi$
$60$		0			0
$61$	21748.1	−	37668.8i	0.748335	−	1.29615i	−0.200285	−	0.979738i	$-0.564187\pi$
$61$	21748.1	−	37668.8i	0.748335	−	1.29615i	0.948620	−	0.316417i	$-0.102480\pi$
$62$		0			0
$63$	−24031.5	+	11116.9i	−0.762834	+	0.352884i
$64$		0			0
$65$	−3443.23	+	5963.84i	−0.101084	+	0.175083i
$66$		0			0
$67$	−16041.2	−	27784.1i	−0.436565	−	0.756154i	0.560857	−	0.827913i	$-0.310472\pi$
$67$	−16041.2	−	27784.1i	−0.436565	−	0.756154i	−0.997422	+	0.0717595i	$0.977139\pi$
$68$		0			0
$69$	−3333.85			−0.0842991
$70$		0			0
$71$	−15820.0			−0.372443			−0.186221	−	0.982508i	$-0.559624\pi$
$71$	−15820.0			−0.372443			−0.186221	+	0.982508i	$0.559624\pi$
$72$		0			0
$73$	−18257.7	−	31623.3i	−0.400996	−	0.694545i	0.592851	−	0.805312i	$-0.298002\pi$
$73$	−18257.7	−	31623.3i	−0.400996	−	0.694545i	−0.993846	+	0.110768i	$0.964669\pi$
$74$		0			0
$75$	−9452.13	+	16371.6i	−0.194033	+	0.336076i
$76$		0			0
$77$	8946.70	−	98786.6i	0.171963	−	1.89877i
$78$		0			0
$79$	12736.1	−	22059.5i	0.229598	−	0.397675i	−0.728091	−	0.685480i	$-0.759592\pi$
$79$	12736.1	−	22059.5i	0.229598	−	0.397675i	0.957689	+	0.287805i	$0.0929256\pi$
$80$		0			0
$81$	−16148.3	−	27969.6i	−0.273472	−	0.473668i
$82$		0			0
$83$	−69443.5			−1.10646			−0.553231	−	0.833028i	$-0.686605\pi$
$83$	−69443.5			−1.10646			−0.553231	+	0.833028i	$0.686605\pi$
$84$		0			0
$85$	4538.91			0.0681404
$86$		0			0
$87$	12276.5	+	21263.5i	0.173890	+	0.301187i
$88$		0			0
$89$	−54165.4	+	93817.2i	−0.724848	+	1.25547i	0.234188	+	0.972191i	$0.424757\pi$
$89$	−54165.4	+	93817.2i	−0.724848	+	1.25547i	−0.959037	+	0.283283i	$0.908577\pi$
$90$		0			0
$91$	−77587.5	−	54681.1i	−0.982173	−	0.692203i
$92$		0			0
$93$	−11403.6	+	19751.6i	−0.136720	+	0.236807i
$94$		0			0
$95$	−12307.4	−	21317.1i	−0.139913	−	0.242337i
$96$		0			0
$97$	94569.1			1.02052			0.510258	−	0.860021i	$-0.329550\pi$
$97$	94569.1			1.02052			0.510258	+	0.860021i	$0.329550\pi$
$98$		0			0
$99$	156269.			1.60245
$100$		0			0
$101$	−73764.5	−	127764.i	−0.719522	−	1.24625i	−0.961189	−	0.275889i	$-0.911028\pi$
$101$	−73764.5	−	127764.i	−0.719522	−	1.24625i	0.241668	−	0.970359i	$-0.422306\pi$
$102$		0			0
$103$	61937.9	−	107280.i	0.575259	−	0.996378i	−0.420754	−	0.907175i	$-0.638234\pi$
$103$	61937.9	−	107280.i	0.575259	−	0.996378i	0.996013	−	0.0892037i	$-0.0284322\pi$
$104$		0			0
$105$	6205.00	+	4373.08i	0.0549248	+	0.0387092i
$106$		0			0
$107$	35341.4	−	61213.0i	0.298417	−	0.516874i	−0.677357	−	0.735655i	$-0.736875\pi$
$107$	35341.4	−	61213.0i	0.298417	−	0.516874i	0.975774	+	0.218781i	$0.0702080\pi$
$108$		0			0
$109$	72065.8	+	124822.i	0.580982	+	1.00629i	0.995363	+	0.0961872i	$0.0306647\pi$
$109$	72065.8	+	124822.i	0.580982	+	1.00629i	−0.414381	+	0.910103i	$0.636002\pi$
$110$		0			0
$111$	−78685.4			−0.606159
$112$		0			0
$113$	−129346.			−0.952919			−0.476459	−	0.879197i	$-0.658080\pi$
$113$	−129346.			−0.952919			−0.476459	+	0.879197i	$0.658080\pi$
$114$		0			0
$115$	−2518.35	−	4361.92i	−0.0177571	−	0.0307562i
$116$		0			0
$117$	74770.1	−	129506.i	0.504968	−	0.874630i
$118$		0			0
$119$	−5642.94	+	62307.6i	−0.0365290	+	0.403342i
$120$		0			0
$121$	−212175.	+	367498.i	−1.31744	+	2.28188i
$122$		0			0
$123$	14986.5	+	25957.4i	0.0893176	+	0.154703i
$124$		0			0
$125$	−57952.4			−0.331739
$126$		0			0
$127$	48800.6			0.268483			0.134241	−	0.990949i	$-0.457140\pi$
$127$	48800.6			0.268483			0.134241	+	0.990949i	$0.457140\pi$
$128$		0			0
$129$	15371.3	+	26624.0i	0.0813275	+	0.140863i
$130$		0			0
$131$	23274.5	−	40312.7i	0.118496	−	0.205241i	−0.800676	−	0.599098i	$-0.795526\pi$
$131$	23274.5	−	40312.7i	0.118496	−	0.205241i	0.919172	+	0.393857i	$0.128859\pi$
$132$		0			0
$133$	307930.	−	142447.i	1.50947	−	0.698273i
$134$		0			0
$135$	−13094.1	+	22679.7i	−0.0618360	+	0.107103i
$136$		0			0
$137$	101393.	+	175618.i	0.461538	+	0.799407i	0.999038	−	0.0438569i	$-0.0139646\pi$
$137$	101393.	+	175618.i	0.461538	+	0.799407i	−0.537500	+	0.843264i	$0.680631\pi$
$138$		0			0
$139$	−146120.			−0.641464			−0.320732	−	0.947170i	$-0.603929\pi$
$139$	−146120.			−0.641464			−0.320732	+	0.947170i	$0.603929\pi$
$140$		0			0
$141$	108356.			0.458994
$142$		0			0
$143$	280098.	+	485144.i	1.14543	+	1.98395i
$144$		0			0
$145$	−18547.1	+	32124.4i	−0.0732580	+	0.126887i
$146$		0			0
$147$	−67745.4	+	79741.9i	−0.258575	+	0.304364i
$148$		0			0
$149$	82600.6	−	143068.i	0.304802	−	0.527932i	−0.672415	−	0.740174i	$-0.734743\pi$
$149$	82600.6	−	143068.i	0.304802	−	0.527932i	0.977217	+	0.212242i	$0.0680765\pi$
$150$		0			0
$151$	58674.6	+	101627.i	0.209415	+	0.362717i	0.951530	−	0.307555i	$-0.0995108\pi$
$151$	58674.6	+	101627.i	0.209415	+	0.362717i	−0.742115	+	0.670272i	$0.766177\pi$
$152$		0			0
$153$	−98563.1			−0.340397
$154$		0			0
$155$	−34456.6			−0.115197
$156$		0			0
$157$	−31453.7	−	54479.4i	−0.101841	−	0.176394i	0.810602	−	0.585597i	$-0.199140\pi$
$157$	−31453.7	−	54479.4i	−0.101841	−	0.176394i	−0.912443	+	0.409203i	$0.865807\pi$
$158$		0			0
$159$	−14500.8	+	25116.1i	−0.0454881	+	0.0787878i
$160$		0			0
$161$	63008.8	−	29147.6i	0.191574	−	0.0886213i
$162$		0			0
$163$	−26029.2	+	45083.8i	−0.0767346	+	0.132908i	−0.901839	−	0.432072i	$-0.857783\pi$
$163$	−26029.2	+	45083.8i	−0.0767346	+	0.132908i	0.825105	+	0.564980i	$0.191116\pi$
$164$		0			0
$165$	−22400.6	−	38799.0i	−0.0640546	−	0.110946i
$166$		0			0
$167$	−572591.			−1.58874			−0.794371	−	0.607433i	$-0.792199\pi$
$167$	−572591.			−1.58874			−0.794371	+	0.607433i	$0.792199\pi$
$168$		0			0
$169$	164783.			0.443809
$170$		0			0
$171$	267258.	+	462904.i	0.698941	+	1.21060i
$172$		0			0
$173$	84629.0	−	146582.i	0.214983	−	0.372361i	−0.738284	−	0.674490i	$-0.764364\pi$
$173$	84629.0	−	146582.i	0.214983	−	0.372361i	0.953267	+	0.302128i	$0.0976971\pi$
$174$		0			0
$175$	35507.0	−	392058.i	0.0876434	−	0.967731i
$176$		0			0
$177$	−101169.	+	175229.i	−0.242724	+	0.420410i
$178$		0			0
$179$	228168.	+	395199.i	0.532258	+	0.921898i	0.999291	+	0.0376580i	$0.0119898\pi$
$179$	228168.	+	395199.i	0.532258	+	0.921898i	−0.467033	+	0.884240i	$0.654677\pi$
$180$		0			0
$181$	243024.			0.551383			0.275692	−	0.961246i	$-0.411093\pi$
$181$	243024.			0.551383			0.275692	+	0.961246i	$0.411093\pi$
$182$		0			0
$183$	270789.			0.597729
$184$		0			0
$185$	−59438.2	−	102950.i	−0.127684	−	0.221155i
$186$		0			0
$187$	184615.	−	319762.i	0.386067	−	0.668688i
$188$		0			0
$189$	−295054.	−	207945.i	−0.600824	−	0.423441i
$190$		0			0
$191$	217787.	−	377218.i	0.431965	−	0.748186i	−0.565077	−	0.825038i	$-0.691154\pi$
$191$	217787.	−	377218.i	0.431965	−	0.748186i	0.997042	+	0.0768522i	$0.0244870\pi$
$192$		0			0
$193$	513274.	+	889016.i	0.991872	+	1.71797i	0.606127	+	0.795368i	$0.292722\pi$
$193$	513274.	+	889016.i	0.991872	+	1.71797i	0.385745	+	0.922605i	$0.373944\pi$
$194$		0			0
$195$	−42872.3			−0.0807403
$196$		0			0
$197$	−147793.			−0.271325			−0.135662	−	0.990755i	$-0.543316\pi$
$197$	−147793.			−0.271325			−0.135662	+	0.990755i	$0.543316\pi$
$198$		0			0
$199$	−502072.	−	869615.i	−0.898739	−	1.55666i	−0.829108	−	0.559089i	$-0.811151\pi$
$199$	−502072.	−	869615.i	−0.898739	−	1.55666i	−0.0696317	−	0.997573i	$-0.522182\pi$
$200$		0			0
$201$	99866.0	−	172973.i	0.174352	−	0.301987i
$202$		0			0
$203$	−417927.	−	294542.i	−0.711805	−	0.501657i
$204$		0			0
$205$	−22641.3	+	39215.9i	−0.0376285	+	0.0651744i
$206$		0			0
$207$	54686.4	+	94719.6i	0.0887061	+	0.153643i
$208$		0			0
$209$	−2.00236e6			−3.17086
$210$		0			0
$211$	95769.0			0.148088			0.0740438	−	0.997255i	$-0.476410\pi$
$211$	95769.0			0.148088			0.0740438	+	0.997255i	$0.476410\pi$
$212$		0			0
$213$	−49244.3	−	85293.7i	−0.0743716	−	0.128815i
$214$		0			0
$215$	−23222.7	+	40222.9i	−0.0342623	+	0.0593441i
$216$		0			0
$217$	42837.7	−	473000.i	0.0617556	−	0.681886i
$218$		0			0
$219$	113665.	−	196874.i	0.160147	−	0.277382i
$220$		0			0
$221$	−176666.	−	305995.i	−0.243317	−	0.421437i
$222$		0			0
$223$	−247314.			−0.333033			−0.166516	−	0.986039i	$-0.553252\pi$
$223$	−247314.			−0.333033			−0.166516	+	0.986039i	$0.553252\pi$
$224$		0			0
$225$	620188.			0.816709
$226$		0			0
$227$	−467787.	−	810230.i	−0.602536	−	1.04362i	−0.992436	−	0.122766i	$-0.960824\pi$
$227$	−467787.	−	810230.i	−0.602536	−	1.04362i	0.389900	−	0.920857i	$-0.372510\pi$
$228$		0			0
$229$	−16910.1	+	29289.2i	−0.0213087	+	0.0369078i	−0.876483	−	0.481433i	$-0.840117\pi$
$229$	−16910.1	+	29289.2i	−0.0213087	+	0.0369078i	0.855174	+	0.518340i	$0.173450\pi$
$230$		0			0
$231$	560460.	−	259267.i	0.691058	−	0.319681i
$232$		0			0
$233$	−65784.0	+	113941.i	−0.0793835	+	0.137496i	−0.902984	−	0.429674i	$-0.858629\pi$
$233$	−65784.0	+	113941.i	−0.0793835	+	0.137496i	0.823601	+	0.567170i	$0.191962\pi$
$234$		0			0
$235$	81851.3	+	141771.i	0.0966843	+	0.167462i
$236$		0			0
$237$	158579.			0.183390
$238$		0			0
$239$	−16742.1			−0.0189590			−0.00947948	−	0.999955i	$-0.503017\pi$
$239$	−16742.1			−0.0189590			−0.00947948	+	0.999955i	$0.503017\pi$
$240$		0			0
$241$	−36714.4	−	63591.2i	−0.0407187	−	0.0705268i	0.844948	−	0.534849i	$-0.179631\pi$
$241$	−36714.4	−	63591.2i	−0.0407187	−	0.0705268i	−0.885667	+	0.464322i	$0.846298\pi$
$242$		0			0
$243$	438831.	−	760078.i	0.476740	−	0.825738i
$244$		0			0
$245$	−155506.	−	28400.1i	−0.165513	−	0.0302276i
$246$		0			0
$247$	−958074.	+	1.65943e6i	−0.999210	+	1.73068i
$248$		0			0
$249$	−216164.	−	374406.i	−0.220945	−	0.382688i
$250$		0			0
$251$	−1.53095e6			−1.53383			−0.766913	−	0.641751i	$-0.778208\pi$
$251$	−1.53095e6			−1.53383			−0.766913	+	0.641751i	$0.778208\pi$
$252$		0			0
$253$	−409724.			−0.402430
$254$		0			0
$255$	14128.7	+	24471.7i	0.0136067	+	0.0235675i
$256$		0			0
$257$	845311.	−	1.46412e6i	0.798333	−	1.38275i	−0.122369	−	0.992485i	$-0.539049\pi$
$257$	845311.	−	1.46412e6i	0.798333	−	1.38275i	0.920701	−	0.390268i	$-0.127618\pi$
$258$		0			0
$259$	1.48713e6	−	687942.i	1.37753	−	0.637239i
$260$		0			0
$261$	402752.	−	697587.i	0.365962	−	0.633865i
$262$		0			0
$263$	492458.	+	852962.i	0.439015	+	0.760397i	0.997614	−	0.0690414i	$-0.0219940\pi$
$263$	492458.	+	852962.i	0.439015	+	0.760397i	−0.558598	+	0.829438i	$0.688661\pi$
$264$		0			0
$265$	−43814.9			−0.0383272
$266$		0			0
$267$	−674424.			−0.578969
$268$		0			0
$269$	918506.	+	1.59090e6i	0.773929	+	1.34048i	0.935394	+	0.353606i	$0.115045\pi$
$269$	918506.	+	1.59090e6i	0.773929	+	1.34048i	−0.161465	+	0.986878i	$0.551622\pi$
$270$		0			0
$271$	244924.	−	424221.i	0.202586	−	0.350889i	−0.746775	−	0.665077i	$-0.768399\pi$
$271$	244924.	−	424221.i	0.202586	−	0.350889i	0.949361	+	0.314188i	$0.101732\pi$
$272$		0			0
$273$	53300.4	−	588526.i	0.0432836	−	0.477924i
$274$		0			0
$275$	−1.16165e6	+	2.01204e6i	−0.926283	+	1.60437i
$276$		0			0
$277$	466781.	+	808488.i	0.365522	+	0.633102i	0.988860	−	0.148850i	$-0.0475572\pi$
$277$	466781.	+	808488.i	0.365522	+	0.633102i	−0.623338	+	0.781953i	$0.714224\pi$
$278$		0			0
$279$	748229.			0.575472
$280$		0			0
$281$	497412.			0.375794			0.187897	−	0.982189i	$-0.439833\pi$
$281$	497412.			0.375794			0.187897	+	0.982189i	$0.439833\pi$
$282$		0			0
$283$	705016.	+	1.22112e6i	0.523278	+	0.906345i	0.999633	+	0.0270916i	$0.00862458\pi$
$283$	705016.	+	1.22112e6i	0.523278	+	0.906345i	−0.476354	+	0.879253i	$0.658042\pi$
$284$		0			0
$285$	76621.2	−	132712.i	0.0558775	−	0.0967827i
$286$		0			0
$287$	−510184.	−	359561.i	−0.365614	−	0.257672i
$288$		0			0
$289$	593487.	−	1.02795e6i	0.417990	−	0.723981i
$290$		0			0
$291$	294375.	+	509872.i	0.203783	+	0.352963i
$292$		0			0
$293$	−2.71744e6			−1.84923			−0.924614	−	0.380905i	$-0.875613\pi$
$293$	−2.71744e6			−1.84923			−0.924614	+	0.380905i	$0.875613\pi$
$294$		0			0
$295$	−305687.			−0.204513
$296$		0			0
$297$	1.06517e6	+	1.84494e6i	0.700696	+	1.21364i
$298$		0			0
$299$	−196041.	+	339554.i	−0.126815	+	0.219650i
$300$		0			0
$301$	−523286.	−	368795.i	−0.332907	−	0.234622i
$302$		0			0
$303$	459228.	−	795407.i	0.287357	−	0.497717i
$304$		0			0
$305$	204552.	+	354294.i	0.125908	+	0.218079i
$306$		0			0
$307$	1.59907e6			0.968324			0.484162	−	0.874978i	$-0.339125\pi$
$307$	1.59907e6			0.968324			0.484162	+	0.874978i	$0.339125\pi$
$308$		0			0
$309$	771202.			0.459485
$310$		0			0
$311$	−1.08487e6	−	1.87904e6i	−0.636027	−	1.10163i	−0.986297	−	0.164982i	$-0.947244\pi$
$311$	−1.08487e6	−	1.87904e6i	−0.636027	−	1.10163i	0.350270	−	0.936649i	$-0.386090\pi$
$312$		0			0
$313$	357778.	−	619690.i	0.206421	−	0.357531i	−0.744164	−	0.667997i	$-0.767152\pi$
$313$	357778.	−	619690.i	0.206421	−	0.357531i	0.950584	+	0.310466i	$0.100485\pi$
$314$		0			0
$315$	22462.8	−	248027.i	0.0127552	−	0.140839i
$316$		0			0
$317$	−1.02241e6	+	1.77086e6i	−0.571448	+	0.989777i	0.424970	+	0.905208i	$0.360285\pi$
$317$	−1.02241e6	+	1.77086e6i	−0.571448	+	0.989777i	−0.996418	+	0.0845692i	$0.973049\pi$
$318$		0			0
$319$	1.50876e6	+	2.61325e6i	0.830124	+	1.43782i
$320$		0			0
$321$	440042.			0.238359
$322$		0			0
$323$	1.26295e6			0.673565
$324$		0			0
$325$	1.11163e6	+	1.92541e6i	0.583786	+	1.01115i
$326$		0			0
$327$	−448653.	+	777089.i	−0.232028	+	0.401885i
$328$		0			0
$329$	−2.04791e6	+	947353.i	−1.04309	+	0.482528i
$330$		0			0
$331$	201242.	−	348562.i	0.100960	−	0.174868i	−0.811120	−	0.584879i	$-0.801142\pi$
$331$	201242.	−	348562.i	0.100960	−	0.174868i	0.912080	+	0.410011i	$0.134475\pi$
$332$		0			0
$333$	1.29071e6	+	2.23557e6i	0.637848	+	1.10479i
$334$		0			0
$335$	301751.			0.146905
$336$		0			0
$337$	3.01447e6			1.44589			0.722946	−	0.690905i	$-0.242788\pi$
$337$	3.01447e6			1.44589			0.722946	+	0.690905i	$0.242788\pi$
$338$		0			0
$339$	−402627.	−	697371.i	−0.190285	−	0.329583i
$340$		0			0
$341$	−1.40148e6	+	2.42743e6i	−0.652681	+	1.13048i
$342$		0			0
$343$	583191.	−	2.09939e6i	0.267655	−	0.963515i
$344$		0			0
$345$	15678.3	−	27155.5i	0.00709170	−	0.0122832i
$346$		0			0
$347$	−1.16028e6	−	2.00967e6i	−0.517298	−	0.895986i	−0.999798	−	0.0200902i	$-0.993605\pi$
$347$	−1.16028e6	−	2.00967e6i	−0.517298	−	0.895986i	0.482501	−	0.875896i	$-0.339729\pi$
$348$		0			0
$349$	−2.81397e6			−1.23668			−0.618338	−	0.785912i	$-0.712194\pi$
$349$	−2.81397e6			−1.23668			−0.618338	+	0.785912i	$0.712194\pi$
$350$		0			0
$351$	2.03862e6			0.883221
$352$		0			0
$353$	−1.08370e6	−	1.87703e6i	−0.462886	−	0.801742i	0.536217	−	0.844080i	$-0.319853\pi$
$353$	−1.08370e6	−	1.87703e6i	−0.462886	−	0.801742i	−0.999103	+	0.0423380i	$0.986519\pi$
$354$		0			0
$355$	74397.3	−	128860.i	0.0313319	−	0.0542684i
$356$		0			0
$357$	−353498.	+	163527.i	−0.146797	+	0.0679077i
$358$		0			0
$359$	−1.75480e6	+	3.03939e6i	−0.718605	+	1.24466i	0.242947	+	0.970039i	$0.421886\pi$
$359$	−1.75480e6	+	3.03939e6i	−0.718605	+	1.24466i	−0.961553	+	0.274621i	$0.911448\pi$
$360$		0			0
$361$	−2.18649e6	−	3.78710e6i	−0.883036	−	1.52946i
$362$		0			0
$363$	−2.64184e6			−1.05230
$364$		0			0
$365$	343446.			0.134936
$366$		0			0
$367$	813276.	+	1.40864e6i	0.315190	+	0.545926i	0.979478	−	0.201551i	$-0.0645983\pi$
$367$	813276.	+	1.40864e6i	0.315190	+	0.545926i	−0.664288	+	0.747477i	$0.731265\pi$
$368$		0			0
$369$	491659.	−	851578.i	0.187974	−	0.325581i
$370$		0			0
$371$	54472.3	−	601466.i	0.0205466	−	0.226870i
$372$		0			0
$373$	430905.	−	746350.i	0.160365	−	0.277761i	−0.774635	−	0.632409i	$-0.782066\pi$
$373$	430905.	−	746350.i	0.160365	−	0.277761i	0.935000	+	0.354649i	$0.115399\pi$
$374$		0			0
$375$	−180394.	−	312452.i	−0.0662436	−	0.114737i
$376$		0			0
$377$	2.88759e6			1.04636
$378$		0			0
$379$	652944.			0.233495			0.116748	−	0.993162i	$-0.462753\pi$
$379$	652944.			0.233495			0.116748	+	0.993162i	$0.462753\pi$
$380$		0			0
$381$	151907.	+	263110.i	0.0536123	+	0.0928592i
$382$		0			0
$383$	1.17055e6	−	2.02745e6i	0.407748	−	0.706241i	−0.586889	−	0.809668i	$-0.699647\pi$
$383$	1.17055e6	−	2.02745e6i	0.407748	−	0.706241i	0.994637	+	0.103427i	$0.0329808\pi$
$384$		0			0
$385$	762583.	+	537444.i	0.262202	+	0.184791i
$386$		0			0
$387$	504285.	−	873446.i	0.171158	−	0.296455i
$388$		0			0
$389$	325648.	+	564038.i	0.109112	+	0.188988i	0.915411	−	0.402521i	$-0.131866\pi$
$389$	325648.	+	564038.i	0.109112	+	0.188988i	−0.806299	+	0.591509i	$0.798533\pi$
$390$		0			0
$391$	258425.			0.0854855
$392$		0			0
$393$	289796.			0.0946478
$394$		0			0
$395$	119789.	+	207481.i	0.0386300	+	0.0669092i
$396$		0			0
$397$	2.08332e6	−	3.60842e6i	0.663408	−	1.14906i	−0.316306	−	0.948657i	$-0.602443\pi$
$397$	2.08332e6	−	3.60842e6i	0.663408	−	1.14906i	0.979714	−	0.200399i	$-0.0642239\pi$
$398$		0			0
$399$	1.72653e6	+	1.21680e6i	0.542929	+	0.382638i
$400$		0			0
$401$	241270.	−	417891.i	0.0749276	−	0.129778i	−0.826127	−	0.563484i	$-0.809461\pi$
$401$	241270.	−	417891.i	0.0749276	−	0.129778i	0.901055	+	0.433705i	$0.142794\pi$
$402$		0			0
$403$	1.34114e6	+	2.32292e6i	0.411349	+	0.712477i
$404$		0			0
$405$	303765.			0.0920239
$406$		0			0
$407$	−9.67030e6			−2.89370
$408$		0			0
$409$	−1.79180e6	−	3.10349e6i	−0.529640	−	0.917364i	−0.999402	−	0.0345708i	$-0.988994\pi$
$409$	−1.79180e6	−	3.10349e6i	−0.529640	−	0.917364i	0.469762	−	0.882793i	$-0.344340\pi$
$410$		0			0
$411$	−631233.	+	1.09333e6i	−0.184325	+	0.319261i
$412$		0			0
$413$	380041.	−	4.19629e6i	0.109637	−	1.21057i
$414$		0			0
$415$	326576.	−	565645.i	0.0930815	−	0.161222i
$416$		0			0
$417$	−454842.	−	787810.i	−0.128092	−	0.221861i
$418$		0			0
$419$	2.66040e6			0.740307			0.370154	−	0.928971i	$-0.379305\pi$
$419$	2.66040e6			0.740307			0.370154	+	0.928971i	$0.379305\pi$
$420$		0			0
$421$	−4.78294e6			−1.31519			−0.657597	−	0.753370i	$-0.728427\pi$
$421$	−4.78294e6			−1.31519			−0.657597	+	0.753370i	$0.728427\pi$
$422$		0			0
$423$	−1.77741e6	−	3.07857e6i	−0.482989	−	0.836562i
$424$		0			0
$425$	732687.	−	1.26905e6i	0.196764	−	0.340805i
$426$		0			0
$427$	−5.11785e6	+	2.36750e6i	−1.35837	+	0.628376i
$428$		0			0
$429$	−1.74378e6	+	3.02031e6i	−0.457455	+	0.792335i
$430$		0			0
$431$	−2.85231e6	−	4.94035e6i	−0.739611	−	1.28104i	−0.952670	−	0.304005i	$-0.901676\pi$
$431$	−2.85231e6	−	4.94035e6i	−0.739611	−	1.28104i	0.213059	−	0.977039i	$-0.431657\pi$
$432$		0			0
$433$	−282700.			−0.0724614			−0.0362307	−	0.999343i	$-0.511535\pi$
$433$	−282700.			−0.0724614			−0.0362307	+	0.999343i	$0.511535\pi$
$434$		0			0
$435$	−230933.			−0.0585144
$436$		0			0
$437$	−700729.	−	1.21370e6i	−0.175528	−	0.304024i
$438$		0			0
$439$	−103638.	+	179506.i	−0.0256660	+	0.0444548i	−0.878573	−	0.477608i	$-0.841504\pi$
$439$	−103638.	+	179506.i	−0.0256660	+	0.0444548i	0.852907	+	0.522063i	$0.174837\pi$
$440$		0			0
$441$	3.37684e6	+	616712.i	0.826826	+	0.151003i
$442$		0			0
$443$	1.71160e6	−	2.96459e6i	0.414376	−	0.717719i	−0.580987	−	0.813913i	$-0.697333\pi$
$443$	1.71160e6	−	2.96459e6i	0.414376	−	0.717719i	0.995363	+	0.0961933i	$0.0306667\pi$
$444$		0			0
$445$	−509453.	−	882399.i	−0.121956	−	0.211234i
$446$		0			0
$447$	1.02848e6			0.243459
$448$		0			0
$449$	−6.36991e6			−1.49114			−0.745568	−	0.666430i	$-0.767822\pi$
$449$	−6.36991e6			−1.49114			−0.745568	+	0.666430i	$0.767822\pi$
$450$		0			0
$451$	1.84181e6	+	3.19012e6i	0.426388	+	0.738525i
$452$		0			0
$453$	−365284.	+	632691.i	−0.0836345	+	0.144859i
$454$		0			0
$455$	810275.	−	374830.i	0.183486	−	0.0848800i
$456$		0			0
$457$	1.82084e6	−	3.15379e6i	0.407832	−	0.706386i	−0.586814	−	0.809722i	$-0.699618\pi$
$457$	1.82084e6	−	3.15379e6i	0.407832	−	0.706386i	0.994647	+	0.103335i	$0.0329514\pi$
$458$		0			0
$459$	−671836.	−	1.16365e6i	−0.148844	−	0.257806i
$460$		0			0
$461$	3.65333e6			0.800639			0.400320	−	0.916376i	$-0.368899\pi$
$461$	3.65333e6			0.800639			0.400320	+	0.916376i	$0.368899\pi$
$462$		0			0
$463$	8.28192e6			1.79547			0.897736	−	0.440533i	$-0.145211\pi$
$463$	8.28192e6			1.79547			0.897736	+	0.440533i	$0.145211\pi$
$464$		0			0
$465$	−107256.	−	185773.i	−0.0230033	−	0.0398429i
$466$		0			0
$467$	907162.	−	1.57125e6i	0.192483	−	0.333390i	−0.753589	−	0.657345i	$-0.771679\pi$
$467$	907162.	−	1.57125e6i	0.192483	−	0.333390i	0.946073	+	0.323955i	$0.105013\pi$
$468$		0			0
$469$	−375148.	+	4.14226e6i	−0.0787536	+	0.869572i
$470$		0			0
$471$	195818.	−	339167.i	0.0406725	−	0.0704468i
$472$		0			0
$473$	1.88911e6	+	3.27204e6i	0.388244	+	0.672459i
$474$		0			0
$475$	−7.94684e6			−1.61607
$476$		0			0
$477$	951447.			0.191465
$478$		0			0
$479$	1.62483e6	+	2.81429e6i	0.323571	+	0.560442i	0.981222	−	0.192881i	$-0.0617832\pi$
$479$	1.62483e6	+	2.81429e6i	0.323571	+	0.560442i	−0.657651	+	0.753323i	$0.728450\pi$
$480$		0			0
$481$	−4.62697e6	+	8.01414e6i	−0.911872	+	1.57941i
$482$		0			0
$483$	353284.	+	248983.i	0.0689058	+	0.0485626i
$484$		0			0
$485$	−444735.	+	770304.i	−0.0858514	+	0.148699i
$486$		0			0
$487$	−1.35060e6	−	2.33931e6i	−0.258051	−	0.446957i	0.707669	−	0.706544i	$-0.249747\pi$
$487$	−1.35060e6	−	2.33931e6i	−0.258051	−	0.446957i	−0.965720	+	0.259587i	$0.916413\pi$
$488$		0			0
$489$	−324094.			−0.0612914
$490$		0			0
$491$	3.57623e6			0.669456			0.334728	−	0.942315i	$-0.391356\pi$
$491$	3.57623e6			0.669456			0.334728	+	0.942315i	$0.391356\pi$
$492$		0			0
$493$	−951618.	−	1.64825e6i	−0.176338	−	0.305426i
$494$		0			0
$495$	−734893.	+	1.27287e6i	−0.134807	+	0.233492i
$496$		0			0
$497$	1.67642e6	+	1.18149e6i	0.304433	+	0.214555i
$498$		0			0
$499$	4.94086e6	−	8.55781e6i	0.888282	−	1.53855i	0.0463764	−	0.998924i	$-0.485233\pi$
$499$	4.94086e6	−	8.55781e6i	0.888282	−	1.53855i	0.841905	−	0.539625i	$-0.181434\pi$
$500$		0			0
$501$	−1.78236e6	−	3.08714e6i	−0.317250	−	0.549493i
$502$		0			0
$503$	1.45199e6			0.255884			0.127942	−	0.991782i	$-0.459163\pi$
$503$	1.45199e6			0.255884			0.127942	+	0.991782i	$0.459163\pi$
$504$		0			0
$505$	1.38759e6			0.242120
$506$		0			0
$507$	512938.	+	888434.i	0.0886226	+	0.153499i
$508$		0			0
$509$	−3.65185e6	+	6.32519e6i	−0.624767	+	1.08213i	0.363819	+	0.931470i	$0.381473\pi$
$509$	−3.65185e6	+	6.32519e6i	−0.624767	+	1.08213i	−0.988586	+	0.150659i	$0.951861\pi$
$510$		0			0
$511$	−426985.	+	4.71463e6i	−0.0723370	+	0.798722i
$512$		0			0
$513$	−3.64342e6	+	6.31059e6i	−0.611246	+	1.05871i
$514$		0			0
$515$	582558.	+	1.00902e6i	0.0967879	+	0.167642i
$516$		0			0
$517$	1.33168e7			2.19116
$518$		0			0
$519$	1.05373e6			0.171716
$520$		0			0
$521$	−978602.	−	1.69499e6i	−0.157947	−	0.273573i	0.776181	−	0.630510i	$-0.217154\pi$
$521$	−978602.	−	1.69499e6i	−0.157947	−	0.273573i	−0.934128	+	0.356937i	$0.883821\pi$
$522$		0			0
$523$	−178071.	+	308427.i	−0.0284667	+	0.0493059i	−0.879908	−	0.475144i	$-0.842396\pi$
$523$	−178071.	+	308427.i	−0.0284667	+	0.0493059i	0.851441	+	0.524450i	$0.175729\pi$
$524$		0			0
$525$	2.22431e6	−	1.02896e6i	0.352207	−	0.162930i
$526$		0			0
$527$	883954.	−	1.53105e6i	0.138645	−	0.240139i
$528$		0			0
$529$	3.07479e6	+	5.32569e6i	0.477723	+	0.827440i
$530$		0			0
$531$	6.63803e6			1.02165
$532$		0			0
$533$	3.52503e6			0.537458
$534$		0			0
$535$	332403.	+	575740.i	0.0502089	+	0.0869644i
$536$		0			0
$537$	−1.42048e6	+	2.46035e6i	−0.212569	+	0.368181i
$538$		0			0
$539$	−8.32579e6	+	9.80014e6i	−1.23439	+	1.45298i
$540$		0			0
$541$	4.89917e6	−	8.48560e6i	0.719663	−	1.24649i	−0.241471	−	0.970408i	$-0.577630\pi$
$541$	4.89917e6	−	8.48560e6i	0.719663	−	1.24649i	0.961133	−	0.276084i	$-0.0890369\pi$
$542$		0			0
$543$	756486.	+	1.31027e6i	0.110104	+	0.190705i
$544$		0			0
$545$	−1.35563e6			−0.195501
$546$		0			0
$547$	1.13688e6			0.162460			0.0812301	−	0.996695i	$-0.474115\pi$
$547$	1.13688e6			0.162460			0.0812301	+	0.996695i	$0.474115\pi$
$548$		0			0
$549$	−4.44187e6	−	7.69354e6i	−0.628977	−	1.08942i
$550$		0			0
$551$	−5.16070e6	+	8.93859e6i	−0.724152	+	1.25427i
$552$		0			0
$553$	−2.99711e6	+	1.38645e6i	−0.416763	+	0.192793i
$554$		0			0
$555$	370038.	−	640925.i	0.0509934	−	0.0883232i
$556$		0			0
$557$	−1.25488e6	−	2.17351e6i	−0.171381	−	0.296841i	0.767522	−	0.641023i	$-0.221490\pi$
$557$	−1.25488e6	−	2.17351e6i	−0.171381	−	0.296841i	−0.938903	+	0.344182i	$0.888156\pi$
$558$		0			0
$559$	3.61555e6			0.489378
$560$		0			0
$561$	2.29868e6			0.308369
$562$		0			0
$563$	4.32848e6	+	7.49715e6i	0.575526	+	0.996839i	0.995984	+	0.0895278i	$0.0285358\pi$
$563$	4.32848e6	+	7.49715e6i	0.575526	+	0.996839i	−0.420459	+	0.907312i	$0.638131\pi$
$564$		0			0
$565$	608281.	−	1.05357e6i	0.0801647	−	0.138849i
$566$		0			0
$567$	−377652.	+	4.16992e6i	−0.0493326	+	0.544715i
$568$		0			0
$569$	−3.62328e6	+	6.27571e6i	−0.469161	+	0.812610i	−0.999378	−	0.0352511i	$-0.988777\pi$
$569$	−3.62328e6	+	6.27571e6i	−0.469161	+	0.812610i	0.530218	+	0.847862i	$0.322110\pi$
$570$		0			0
$571$	−4.00743e6	−	6.94107e6i	−0.514370	−	0.890915i	−0.999861	−	0.0166736i	$-0.994692\pi$
$571$	−4.00743e6	−	6.94107e6i	−0.514370	−	0.890915i	0.485491	−	0.874242i	$-0.338641\pi$
$572$		0			0
$573$	2.71171e6			0.345030
$574$		0			0
$575$	−1.62608e6			−0.205104
$576$		0			0
$577$	2.25978e6	+	3.91406e6i	0.282571	+	0.489426i	0.972017	−	0.234910i	$-0.0754796\pi$
$577$	2.25978e6	+	3.91406e6i	0.282571	+	0.489426i	−0.689447	+	0.724337i	$0.742146\pi$
$578$		0			0
$579$	−3.19544e6	+	5.53466e6i	−0.396126	+	0.686111i
$580$		0			0
$581$	7.35884e6	+	5.18627e6i	0.904418	+	0.637404i
$582$		0			0
$583$	−1.78212e6	+	3.08672e6i	−0.217153	+	0.376120i
$584$		0			0
$585$	703251.	+	1.21807e6i	0.0849612	+	0.147157i
$586$		0			0
$587$	−2.07729e6			−0.248830			−0.124415	−	0.992230i	$-0.539705\pi$
$587$	−2.07729e6			−0.248830			−0.124415	+	0.992230i	$0.539705\pi$
$588$		0			0
$589$	−9.58750e6			−1.13872
$590$		0			0
$591$	−460051.	−	796832.i	−0.0541798	−	0.0938421i
$592$		0			0
$593$	6.33236e6	−	1.09680e7i	0.739484	−	1.28082i	−0.213244	−	0.976999i	$-0.568403\pi$
$593$	6.33236e6	−	1.09680e7i	0.739484	−	1.28082i	0.952728	−	0.303825i	$-0.0982637\pi$
$594$		0			0
$595$	−480983.	−	338981.i	−0.0556978	−	0.0392540i
$596$		0			0
$597$	3.12570e6	−	5.41387e6i	0.358932	−	0.621688i
$598$		0			0
$599$	1.69926e6	+	2.94321e6i	0.193505	+	0.335161i	0.946410	−	0.322969i	$-0.104681\pi$
$599$	1.69926e6	+	2.94321e6i	0.193505	+	0.335161i	−0.752904	+	0.658130i	$0.771348\pi$
$600$		0			0
$601$	8.79425e6			0.993145			0.496572	−	0.867995i	$-0.334592\pi$
$601$	8.79425e6			0.993145			0.496572	+	0.867995i	$0.334592\pi$
$602$		0			0
$603$	−6.55256e6			−0.733868
$604$		0			0
$605$	−1.99562e6	−	3.45651e6i	−0.221661	−	0.383928i
$606$		0			0
$607$	3.07428e6	−	5.32480e6i	0.338666	−	0.586586i	−0.645516	−	0.763746i	$-0.723358\pi$
$607$	3.07428e6	−	5.32480e6i	0.338666	−	0.586586i	0.984182	+	0.177160i	$0.0566911\pi$
$608$		0			0
$609$	287104.	−	3.17012e6i	0.0313687	−	0.346363i
$610$		0			0
$611$	6.37172e6	−	1.10361e7i	0.690484	−	1.19595i
$612$		0			0
$613$	−7.12851e6	−	1.23469e7i	−0.766210	−	1.32711i	−0.939605	−	0.342262i	$-0.888807\pi$
$613$	−7.12851e6	−	1.23469e7i	−0.766210	−	1.32711i	0.173395	−	0.984852i	$-0.444526\pi$
$614$		0			0
$615$	−281911.			−0.0300555
$616$		0			0
$617$	−1.26910e7			−1.34210			−0.671048	−	0.741414i	$-0.734156\pi$
$617$	−1.26910e7			−1.34210			−0.671048	+	0.741414i	$0.734156\pi$
$618$		0			0
$619$	2.40398e6	+	4.16381e6i	0.252176	+	0.436782i	0.964125	−	0.265450i	$-0.0855204\pi$
$619$	2.40398e6	+	4.16381e6i	0.252176	+	0.436782i	−0.711949	+	0.702232i	$0.752187\pi$
$620$		0			0
$621$	−745518.	+	1.29128e6i	−0.0775763	+	0.134366i
$622$		0			0
$623$	1.27464e7	−	5.89645e6i	1.31574	−	0.608654i
$624$		0			0
$625$	−4.47205e6	+	7.74582e6i	−0.457938	+	0.793172i
$626$		0			0
$627$	−6.23295e6	−	1.07958e7i	−0.633177	−	1.09669i
$628$		0			0
$629$	6.09934e6			0.614690
$630$		0			0
$631$	−1.89817e7			−1.89785			−0.948925	−	0.315501i	$-0.897827\pi$
$631$	−1.89817e7			−1.89785			−0.948925	+	0.315501i	$0.897827\pi$
$632$		0			0
$633$	298110.	+	516341.i	0.0295710	+	0.0512186i
$634$		0			0
$635$	−229497.	+	397501.i	−0.0225862	+	0.0391205i
$636$		0			0
$637$	4.13808e6	+	1.15890e7i	0.404065	+	1.13161i
$638$		0			0
$639$	−1.61555e6	+	2.79821e6i	−0.156519	+	0.271099i
$640$		0			0
$641$	−5.51275e6	−	9.54836e6i	−0.529935	−	0.917875i	−0.999390	−	0.0349184i	$-0.988883\pi$
$641$	−5.51275e6	−	9.54836e6i	−0.529935	−	0.917875i	0.469455	−	0.882956i	$-0.344450\pi$
$642$		0			0
$643$	−4.19154e6			−0.399803			−0.199901	−	0.979816i	$-0.564062\pi$
$643$	−4.19154e6			−0.399803			−0.199901	+	0.979816i	$0.564062\pi$
$644$		0			0
$645$	−289151.			−0.0273669
$646$		0			0
$647$	−7.97441e6	−	1.38121e7i	−0.748924	−	1.29718i	−0.948339	−	0.317260i	$-0.897237\pi$
$647$	−7.97441e6	−	1.38121e7i	−0.748924	−	1.29718i	0.199414	−	0.979915i	$-0.436096\pi$
$648$		0			0
$649$	−1.24334e7	+	2.15354e7i	−1.15872	+	2.00697i
$650$		0			0
$651$	2.68354e6	−	1.24139e6i	0.248173	−	0.114804i
$652$		0			0
$653$	4.90384e6	−	8.49370e6i	0.450042	−	0.779496i	−0.548346	−	0.836252i	$-0.684742\pi$
$653$	4.90384e6	−	8.49370e6i	0.450042	−	0.779496i	0.998388	+	0.0567558i	$0.0180756\pi$
$654$		0			0
$655$	218909.	+	379161.i	0.0199370	+	0.0345319i
$656$		0			0
$657$	−7.45799e6			−0.674075
$658$		0			0
$659$	1.12535e7			1.00943			0.504714	−	0.863287i	$-0.331598\pi$
$659$	1.12535e7			1.00943			0.504714	+	0.863287i	$0.331598\pi$
$660$		0			0
$661$	−1.88024e6	−	3.25668e6i	−0.167383	−	0.289915i	0.770116	−	0.637904i	$-0.220198\pi$
$661$	−1.88024e6	−	3.25668e6i	−0.167383	−	0.289915i	−0.937499	+	0.347988i	$0.886865\pi$
$662$		0			0
$663$	1.09985e6	−	1.90500e6i	0.0971741	−	0.168310i
$664$		0			0
$665$	−287829.	+	3.17811e6i	−0.0252394	+	0.278686i
$666$		0			0
$667$	−1.05598e6	+	1.82902e6i	−0.0919057	+	0.159185i
$668$		0			0
$669$	−769840.	−	1.33340e6i	−0.0665021	−	0.115185i
$670$		0			0
$671$	3.32796e7			2.85346
$672$		0			0
$673$	4.12878e6			0.351386			0.175693	−	0.984445i	$-0.443783\pi$
$673$	4.12878e6			0.351386			0.175693	+	0.984445i	$0.443783\pi$
$674$		0			0
$675$	4.22739e6	+	7.32205e6i	0.357119	+	0.618548i
$676$		0			0
$677$	3.78820e6	−	6.56135e6i	0.317659	−	0.550202i	−0.662340	−	0.749203i	$-0.730437\pi$
$677$	3.78820e6	−	6.56135e6i	0.317659	−	0.550202i	0.979999	+	0.199002i	$0.0637699\pi$
$678$		0			0
$679$	−1.00214e7	−	7.06274e6i	−0.834167	−	0.587894i
$680$		0			0
$681$	2.91225e6	−	5.04417e6i	0.240636	−	0.416794i
$682$		0			0
$683$	−7.49724e6	−	1.29856e7i	−0.614964	−	1.06515i	−0.990391	−	0.138297i	$-0.955837\pi$
$683$	−7.49724e6	−	1.29856e7i	−0.614964	−	1.06515i	0.375427	−	0.926852i	$-0.377496\pi$
$684$		0			0
$685$	−1.90731e6			−0.155308
$686$		0			0
$687$	−210551.			−0.0170202
$688$		0			0
$689$	1.70539e6	+	2.95382e6i	0.136860	+	0.237048i
$690$		0			0
$691$	5.51490e6	−	9.55209e6i	0.439382	−	0.761032i	−0.558260	−	0.829666i	$-0.688531\pi$
$691$	5.51490e6	−	9.55209e6i	0.439382	−	0.761032i	0.997642	+	0.0686340i	$0.0218641\pi$
$692$		0			0
$693$	−1.65596e7	−	1.16707e7i	−1.30984	−	0.923129i
$694$		0			0
$695$	687166.	−	1.19021e6i	0.0539635	−	0.0934675i
$696$		0			0
$697$	−1.16169e6	−	2.01210e6i	−0.0905746	−	0.156880i
$698$		0			0
$699$	−819089.			−0.0634072
$700$		0			0
$701$	1.77997e7			1.36810			0.684048	−	0.729437i	$-0.260218\pi$
$701$	1.77997e7			1.36810			0.684048	+	0.729437i	$0.260218\pi$
$702$		0			0
$703$	−1.65386e7	−	2.86457e7i	−1.26215	−	2.18611i
$704$		0			0
$705$	−509573.	+	882607.i	−0.0386130	+	0.0668797i
$706$		0			0
$707$	−1.72510e6	+	1.90480e7i	−0.129797	+	1.43318i
$708$		0			0
$709$	−6.13375e6	+	1.06240e7i	−0.458259	+	0.793727i	−0.998869	−	0.0475457i	$-0.984860\pi$
$709$	−6.13375e6	+	1.06240e7i	−0.458259	+	0.793727i	0.540610	+	0.841273i	$0.318193\pi$
$710$		0			0
$711$	−2.60124e6	−	4.50548e6i	−0.192977	−	0.334247i
$712$		0			0
$713$	−1.96180e6			−0.144521
$714$		0			0
$715$	−5.26893e6			−0.385441
$716$		0			0
$717$	−52114.7	−	90265.4i	−0.00378584	−	0.00655727i
$718$		0			0
$719$	−8.34886e6	+	1.44606e7i	−0.602289	+	1.04319i	0.390185	+	0.920736i	$0.372411\pi$
$719$	−8.34886e6	+	1.44606e7i	−0.602289	+	1.04319i	−0.992474	+	0.122458i	$0.960922\pi$
$720$		0			0
$721$	−1.45755e7	+	6.74257e6i	−1.04420	+	0.483045i
$722$		0			0
$723$	228569.	−	395893.i	0.0162619	−	0.0281665i
$724$		0			0
$725$	5.98785e6	+	1.03713e7i	0.423084	+	0.732802i
$726$		0			0
$727$	−1.75983e6			−0.123491			−0.0617455	−	0.998092i	$-0.519667\pi$
$727$	−1.75983e6			−0.123491			−0.0617455	+	0.998092i	$0.519667\pi$
$728$		0			0
$729$	−2.38409e6			−0.166151
$730$		0			0
$731$	−1.19152e6	−	2.06377e6i	−0.0824721	−	0.142846i
$732$		0			0
$733$	4.85468e6	−	8.40856e6i	0.333734	−	0.578045i	−0.649506	−	0.760356i	$-0.725024\pi$
$733$	4.85468e6	−	8.40856e6i	0.333734	−	0.578045i	0.983241	+	0.182311i	$0.0583578\pi$
$734$		0			0
$735$	−330940.	−	926820.i	−0.0225960	−	0.0632815i
$736$		0			0
$737$	1.22734e7	−	2.12581e7i	0.832328	−	1.44163i
$738$		0			0
$739$	6.74097e6	+	1.16757e7i	0.454058	+	0.786452i	0.998634	−	0.0522600i	$-0.0166424\pi$
$739$	6.74097e6	+	1.16757e7i	0.454058	+	0.786452i	−0.544575	+	0.838712i	$0.683309\pi$
$740$		0			0
$741$	−1.19292e7			−0.798114
$742$		0			0
$743$	4.67927e6			0.310961			0.155481	−	0.987839i	$-0.450307\pi$
$743$	4.67927e6			0.310961			0.155481	+	0.987839i	$0.450307\pi$
$744$		0			0
$745$	776900.	+	1.34563e6i	0.0512831	+	0.0888250i
$746$		0			0
$747$	−7.09163e6	+	1.22831e7i	−0.464991	+	0.805388i
$748$		0			0
$749$	−8.31668e6	+	3.84726e6i	−0.541683	+	0.250581i
$750$		0			0
$751$	−1.13364e7	+	1.96353e7i	−0.733460	+	1.27039i	0.221935	+	0.975061i	$0.428763\pi$
$751$	−1.13364e7	+	1.96353e7i	−0.733460	+	1.27039i	−0.955396	+	0.295329i	$0.904571\pi$
$752$		0			0
$753$	−4.76554e6	−	8.25415e6i	−0.306284	−	0.530499i
$754$		0			0
$755$	−1.10373e6			−0.0704684
$756$		0			0
$757$	1.81102e6			0.114864			0.0574320	−	0.998349i	$-0.481709\pi$
$757$	1.81102e6			0.114864			0.0574320	+	0.998349i	$0.481709\pi$
$758$		0			0
$759$	−1.27539e6	−	2.20904e6i	−0.0803597	−	0.139187i
$760$		0			0
$761$	5.69775e6	−	9.86880e6i	0.356650	−	0.617735i	−0.630749	−	0.775987i	$-0.717252\pi$
$761$	5.69775e6	−	9.86880e6i	0.356650	−	0.617735i	0.987399	+	0.158251i	$0.0505856\pi$
$762$		0			0
$763$	1.68537e6	−	1.86093e7i	0.104805	−	1.15723i
$764$		0			0
$765$	463518.	−	802837.i	0.0286361	−	0.0495991i
$766$		0			0
$767$	1.18981e7	+	2.06081e7i	0.730280	+	1.26488i
$768$		0			0
$769$	3.12982e7			1.90855			0.954274	−	0.298933i	$-0.0966308\pi$
$769$	3.12982e7			1.90855			0.954274	+	0.298933i	$0.0966308\pi$
$770$		0			0
$771$	1.05251e7			0.637664
$772$		0			0
$773$	1.27649e7	+	2.21095e7i	0.768369	+	1.33085i	0.938447	+	0.345423i	$0.112265\pi$
$773$	1.27649e7	+	2.21095e7i	0.768369	+	1.33085i	−0.170078	+	0.985431i	$0.554402\pi$
$774$		0			0
$775$	−5.56209e6	+	9.63383e6i	−0.332647	+	0.576162i
$776$		0			0
$777$	8.33820e6	+	5.87649e6i	0.495473	+	0.349193i
$778$		0			0
$779$	−6.29992e6	+	1.09118e7i	−0.371956	+	0.644246i
$780$		0			0
$781$	−6.05204e6	−	1.04824e7i	−0.355038	−	0.614943i
$782$		0			0
$783$	1.09811e7			0.640091
$784$		0			0
$785$	591676.			0.0342697
$786$		0			0
$787$	7.87867e6	+	1.36462e7i	0.453436	+	0.785374i	0.998597	−	0.0529575i	$-0.0168648\pi$
$787$	7.87867e6	+	1.36462e7i	0.453436	+	0.785374i	−0.545161	+	0.838331i	$0.683531\pi$
$788$		0			0
$789$	−3.06585e6	+	5.31020e6i	−0.175331	+	0.303681i
$790$		0			0
$791$	1.37066e7	+	9.65997e6i	0.778913	+	0.548952i
$792$		0			0
$793$	1.59233e7	−	2.75800e7i	0.899189	−	1.55744i
$794$		0			0
$795$	−136387.	−	236229.i	−0.00765342	−	0.0132561i
$796$		0			0
$797$	−1.28373e7			−0.715858			−0.357929	−	0.933749i	$-0.616517\pi$
$797$	−1.28373e7			−0.715858			−0.357929	+	0.933749i	$0.616517\pi$
$798$		0			0
$799$	−8.39930e6			−0.465453
$800$		0			0
$801$	1.10628e7	+	1.91614e7i	0.609236	+	1.05523i
$802$		0			0
$803$	1.39693e7	−	2.41955e7i	0.764513	−	1.32418i
$804$		0			0
$805$	−58895.6	+	650306.i	−0.00320327	+	0.0353694i
$806$		0			0
$807$	−5.71825e6	+	9.90430e6i	−0.309086	+	0.535352i
$808$		0			0
$809$	−582848.	−	1.00952e6i	−0.0313101	−	0.0542306i	0.849946	−	0.526870i	$-0.176635\pi$
$809$	−582848.	−	1.00952e6i	−0.0313101	−	0.0542306i	−0.881256	+	0.472640i	$0.843301\pi$
$810$		0			0
$811$	−4.99526e6			−0.266690			−0.133345	−	0.991070i	$-0.542572\pi$
$811$	−4.99526e6			−0.266690			−0.133345	+	0.991070i	$0.542572\pi$
$812$		0			0
$813$	3.04960e6			0.161814
$814$		0			0
$815$	−244818.	−	424036.i	−0.0129107	−	0.0223619i
$816$		0			0
$817$	−6.46170e6	+	1.11920e7i	−0.338681	+	0.586614i
$818$		0			0
$819$	−1.75952e7	+	8.13948e6i	−0.916611	+	0.424021i
$820$		0			0
$821$	−9.04370e6	+	1.56642e7i	−0.468261	+	0.811052i	−0.999342	−	0.0362688i	$-0.988453\pi$
$821$	−9.04370e6	+	1.56642e7i	−0.468261	+	0.811052i	0.531081	+	0.847321i	$0.321786\pi$
$822$		0			0
$823$	6.04730e6	+	1.04742e7i	0.311216	+	0.539042i	0.978626	−	0.205649i	$-0.0659304\pi$
$823$	6.04730e6	+	1.04742e7i	0.311216	+	0.539042i	−0.667410	+	0.744691i	$0.732597\pi$
$824$		0			0
$825$	−1.44639e7			−0.739864
$826$		0			0
$827$	−1.22010e7			−0.620345			−0.310172	−	0.950680i	$-0.600387\pi$
$827$	−1.22010e7			−0.620345			−0.310172	+	0.950680i	$0.600387\pi$
$828$		0			0
$829$	1.06077e7	+	1.83731e7i	0.536088	+	0.928531i	0.999110	+	0.0421846i	$0.0134318\pi$
$829$	1.06077e7	+	1.83731e7i	0.536088	+	0.928531i	−0.463022	+	0.886347i	$0.653235\pi$
$830$		0			0
$831$	−2.90599e6	+	5.03332e6i	−0.145979	+	0.252844i
$832$		0			0
$833$	5.25132e6	−	6.18123e6i	0.262214	−	0.308647i
$834$		0			0
$835$	2.69275e6	−	4.66399e6i	0.133654	−	0.231495i
$836$		0			0
$837$	5.10016e6	+	8.83373e6i	0.251634	+	0.435843i
$838$		0			0
$839$	4.68317e6			0.229686			0.114843	−	0.993384i	$-0.463363\pi$
$839$	4.68317e6			0.229686			0.114843	+	0.993384i	$0.463363\pi$
$840$		0			0
$841$	−4.95703e6			−0.241675
$842$		0			0
$843$	1.54834e6	+	2.68181e6i	0.0750409	+	0.129975i
$844$		0			0
$845$	−774936.	+	1.34223e6i	−0.0373357	+	0.0646673i
$846$		0			0
$847$	4.99300e7	−	2.30974e7i	2.39140	−	1.10625i
$848$		0			0
$849$	−4.38915e6	+	7.60223e6i	−0.208983	+	0.361969i
$850$		0			0
$851$	−3.38413e6	−	5.86149e6i	−0.160186	−	0.277450i
$852$		0			0
$853$	−1.03858e7			−0.488729			−0.244364	−	0.969684i	$-0.578579\pi$
$853$	−1.03858e7			−0.488729			−0.244364	+	0.969684i	$0.578579\pi$
$854$		0			0
$855$	−5.02739e6			−0.235195
$856$		0			0
$857$	4.71729e6	+	8.17059e6i	0.219402	+	0.380015i	0.954625	−	0.297810i	$-0.0962560\pi$
$857$	4.71729e6	+	8.17059e6i	0.219402	+	0.380015i	−0.735223	+	0.677825i	$0.762923\pi$
$858$		0			0
$859$	−3.54215e6	+	6.13518e6i	−0.163789	+	0.283690i	−0.936224	−	0.351403i	$-0.885705\pi$
$859$	−3.54215e6	+	6.13518e6i	−0.163789	+	0.283690i	0.772436	+	0.635093i	$0.219038\pi$
$860$		0			0
$861$	350482.	−	3.86991e6i	0.0161123	−	0.177907i
$862$		0			0
$863$	−4.55307e6	+	7.88616e6i	−0.208103	+	0.360444i	−0.951117	−	0.308831i	$-0.900062\pi$
$863$	−4.55307e6	+	7.88616e6i	−0.208103	+	0.360444i	0.743014	+	0.669276i	$0.233395\pi$
$864$		0			0
$865$	795979.	+	1.37868e6i	0.0361710	+	0.0626501i
$866$		0			0
$867$	7.38962e6			0.333868
$868$		0			0
$869$	1.94891e7			0.875474
$870$		0			0
$871$	−1.17449e7	−	2.03428e7i	−0.524571	−	0.908584i
$872$		0			0
$873$	9.65749e6	−	1.67273e7i	0.428873	−	0.742830i
$874$		0			0
$875$	6.14115e6	+	4.32808e6i	0.271162	+	0.191106i
$876$		0			0
$877$	−1.42369e7	+	2.46590e7i	−0.625052	+	1.08262i	0.363479	+	0.931602i	$0.381589\pi$
$877$	−1.42369e7	+	2.46590e7i	−0.625052	+	1.08262i	−0.988531	+	0.151019i	$0.951744\pi$
$878$		0			0
$879$	−8.45884e6	−	1.46511e7i	−0.369265	−	0.639586i
$880$		0			0
$881$	−5.51673e6			−0.239465			−0.119732	−	0.992806i	$-0.538204\pi$
$881$	−5.51673e6			−0.239465			−0.119732	+	0.992806i	$0.538204\pi$
$882$		0			0
$883$	1.82256e7			0.786647			0.393323	−	0.919400i	$-0.371325\pi$
$883$	1.82256e7			0.786647			0.393323	+	0.919400i	$0.371325\pi$
$884$		0			0
$885$	−951542.	−	1.64812e6i	−0.0408385	−	0.0707344i
$886$		0			0
$887$	1.87391e7	−	3.24570e7i	0.799722	−	1.38516i	−0.120075	−	0.992765i	$-0.538313\pi$
$887$	1.87391e7	−	3.24570e7i	0.799722	−	1.38516i	0.919797	−	0.392395i	$-0.128353\pi$
$888$		0			0
$889$	−5.17135e6	−	3.64459e6i	−0.219457	−	0.154666i
$890$		0			0
$891$	1.23553e7	−	2.14000e7i	0.521385	−	0.903066i
$892$		0			0
$893$	2.27750e7	+	3.94475e7i	0.955720	+	1.65536i
$894$		0			0
$895$	−4.29207e6			−0.179106
$896$		0			0
$897$	−2.44095e6			−0.101293
$898$		0			0
$899$	7.22408e6	+	1.25125e7i	0.298115	+	0.516350i
$900$		0			0
$901$	1.12403e6	−	1.94688e6i	0.0461283	−	0.0798966i
$902$		0			0
$903$	359483.	−	3.96929e6i	0.0146710	−	0.161992i
$904$		0			0
$905$	−1.14288e6	+	1.97953e6i	−0.0463853	+	0.0803418i
$906$		0			0
$907$	1.46548e7	+	2.53828e7i	0.591508	+	1.02452i	0.994030	+	0.109112i	$0.0348006\pi$
$907$	1.46548e7	+	2.53828e7i	0.591508	+	1.02452i	−0.402521	+	0.915411i	$0.631866\pi$
$908$		0			0
$909$	−3.01316e7			−1.20952
$910$		0			0
$911$	−2.86518e7			−1.14382			−0.571908	−	0.820318i	$-0.693797\pi$
$911$	−2.86518e7			−1.14382			−0.571908	+	0.820318i	$0.693797\pi$
$912$		0			0
$913$	−2.65661e7	−	4.60139e7i	−1.05475	−	1.82689i
$914$		0			0
$915$	−1.27346e6	+	2.20569e6i	−0.0502842	+	0.0870947i
$916$		0			0
$917$	−5.47706e6	+	2.53367e6i	−0.215092	+	0.0995007i
$918$		0			0
$919$	−2.21076e7	+	3.82916e7i	−0.863483	+	1.49560i	0.00506296	+	0.999987i	$0.498388\pi$
$919$	−2.21076e7	+	3.82916e7i	−0.863483	+	1.49560i	−0.868546	+	0.495609i	$0.834945\pi$
$920$		0			0
$921$	4.97757e6	+	8.62141e6i	0.193361	+	0.334911i
$922$		0			0
$923$	−1.15829e7			−0.447522
$924$		0			0
$925$	−3.83788e7			−1.47481
$926$		0			0
$927$	−1.26503e7	−	2.19110e7i	−0.483506	−	0.837458i
$928$		0			0
$929$	1.53279e7	−	2.65487e7i	0.582698	−	1.00926i	−0.412460	−	0.910976i	$-0.635330\pi$
$929$	1.53279e7	−	2.65487e7i	0.582698	−	1.00926i	0.995158	−	0.0982867i	$-0.0313362\pi$
$930$		0			0
$931$	−4.32695e7	−	7.90229e6i	−1.63609	−	0.298799i
$932$		0			0
$933$	6.75394e6	−	1.16982e7i	0.254011	−	0.439961i
$934$		0			0
$935$	1.73640e6	+	3.00753e6i	0.0649561	+	0.112507i
$936$		0			0
$937$	−1.26278e6			−0.0469871			−0.0234935	−	0.999724i	$-0.507479\pi$
$937$	−1.26278e6			−0.0469871			−0.0234935	+	0.999724i	$0.507479\pi$
$938$		0			0
$939$	4.45477e6			0.164877
$940$		0			0
$941$	−3.75600e6	−	6.50558e6i	−0.138278	−	0.239504i	0.788567	−	0.614949i	$-0.210823\pi$
$941$	−3.75600e6	−	6.50558e6i	−0.138278	−	0.239504i	−0.926845	+	0.375445i	$0.877490\pi$
$942$		0			0
$943$	−1.28909e6	+	2.23277e6i	−0.0472068	+	0.0817645i
$944$		0			0
$945$	3.08136e6	−	1.42543e6i	0.112244	−	0.0519236i
$946$		0			0
$947$	1.88665e7	−	3.26777e7i	0.683622	−	1.18407i	−0.290245	−	0.956952i	$-0.593737\pi$
$947$	1.88665e7	−	3.26777e7i	0.683622	−	1.18407i	0.973868	−	0.227117i	$-0.0729298\pi$
$948$		0			0
$949$	−1.33678e7	−	2.31537e7i	−0.481831	−	0.834555i
$950$		0			0
$951$	−1.27302e7			−0.456441
$952$		0			0
$953$	3.21132e7			1.14538			0.572692	−	0.819771i	$-0.305899\pi$
$953$	3.21132e7			1.14538			0.572692	+	0.819771i	$0.305899\pi$
$954$		0			0
$955$	2.04840e6	+	3.54793e6i	0.0726785	+	0.125883i
$956$		0			0
$957$	−9.39293e6	+	1.62690e7i	−0.331529	+	0.574224i
$958$		0			0
$959$	2.37123e6	−	2.61824e7i	0.0832584	−	0.919313i
$960$		0			0
$961$	7.60416e6	−	1.31708e7i	0.265609	−	0.460048i
$962$		0			0
$963$	−7.21819e6	−	1.25023e7i	−0.250820	−	0.434433i
$964$		0			0
$965$	−9.65520e6			−0.333767
$966$		0			0
$967$	4.33133e7			1.48955			0.744775	−	0.667315i	$-0.232557\pi$
$967$	4.33133e7			1.48955			0.744775	+	0.667315i	$0.232557\pi$
$968$		0			0
$969$	3.93130e6	+	6.80922e6i	0.134502	+	0.232963i
$970$		0			0
$971$	3.67358e6	−	6.36283e6i	0.125038	−	0.216572i	−0.796710	−	0.604362i	$-0.793428\pi$
$971$	3.67358e6	−	6.36283e6i	0.125038	−	0.216572i	0.921748	+	0.387790i	$0.126761\pi$
$972$		0			0
$973$	1.54842e7	+	1.09127e7i	0.524331	+	0.369531i
$974$		0			0
$975$	−6.92059e6	+	1.19868e7i	−0.233148	+	0.403824i
$976$		0			0
$977$	−1.57272e7	−	2.72403e7i	−0.527126	−	0.913009i	−0.999500	−	0.0316109i	$-0.989936\pi$
$977$	−1.57272e7	−	2.72403e7i	−0.527126	−	0.913009i	0.472374	−	0.881398i	$-0.343397\pi$
$978$		0			0
$979$	−8.28856e7			−2.76390
$980$		0			0
$981$	2.94377e7			0.976633
$982$		0			0
$983$	5.48935e6	+	9.50784e6i	0.181191	+	0.313832i	0.942286	−	0.334808i	$-0.108671\pi$
$983$	5.48935e6	+	9.50784e6i	0.181191	+	0.313832i	−0.761095	+	0.648640i	$0.775338\pi$
$984$		0			0
$985$	695036.	−	1.20384e6i	0.0228253	−	0.0395346i
$986$		0			0
$987$	−1.14824e7	−	8.09242e6i	−0.375180	−	0.264415i
$988$		0			0
$989$	−1.32219e6	+	2.29011e6i	−0.0429838	+	0.0744501i
$990$		0			0
$991$	2.73306e7	+	4.73380e7i	0.884026	+	1.53118i	0.846826	+	0.531870i	$0.178510\pi$
$991$	2.73306e7	+	4.73380e7i	0.884026	+	1.53118i	0.0371998	+	0.999308i	$0.488156\pi$
$992$		0			0
$993$	2.50571e6			0.0806413
$994$		0			0
$995$	9.44449e6			0.302427
$996$		0			0
$997$	−2.78746e7	−	4.82803e7i	−0.888120	−	1.53827i	−0.842096	−	0.539328i	$-0.818678\pi$
$997$	−2.78746e7	−	4.82803e7i	−0.888120	−	1.53827i	−0.0460238	−	0.998940i	$-0.514655\pi$
$998$		0			0
$999$	−1.75957e7	+	3.04767e7i	−0.557819	+	0.966170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.6.i.g.65.3		10
4.3	odd	2		56.6.i.a.9.3	✓	10
7.2	even	3		784.6.a.bj.1.3		5
7.4	even	3	inner	112.6.i.g.81.3		10
7.5	odd	6		784.6.a.bm.1.3		5
12.11	even	2		504.6.s.d.289.3		10
28.3	even	6		392.6.i.p.361.3		10
28.11	odd	6		56.6.i.a.25.3	yes	10
28.19	even	6		392.6.a.i.1.3		5
28.23	odd	6		392.6.a.l.1.3		5
28.27	even	2		392.6.i.p.177.3		10
84.11	even	6		504.6.s.d.361.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.6.i.a.9.3	✓	10	4.3	odd	2
56.6.i.a.25.3	yes	10	28.11	odd	6
112.6.i.g.65.3		10	1.1	even	1	trivial
112.6.i.g.81.3		10	7.4	even	3	inner
392.6.a.i.1.3		5	28.19	even	6
392.6.a.l.1.3		5	28.23	odd	6
392.6.i.p.177.3		10	28.27	even	2
392.6.i.p.361.3		10	28.3	even	6
504.6.s.d.289.3		10	12.11	even	2
504.6.s.d.361.3		10	84.11	even	6
784.6.a.bj.1.3		5	7.2	even	3
784.6.a.bm.1.3		5	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.11280 + 5.39153i) q^{3} +(-4.70275 + 8.14541i) q^{5} +(-105.969 - 74.6834i) q^{7} +(102.121 - 176.879i) q^{9} +O(q^{10})\)	\(q+(3.11280 + 5.39153i) q^{3} +(-4.70275 + 8.14541i) q^{5} +(-105.969 - 74.6834i) q^{7} +(102.121 - 176.879i) q^{9} +(382.558 + 662.609i) q^{11} +732.172 q^{13} -58.5549 q^{15} +(-241.290 - 417.927i) q^{17} +(-1308.54 + 2266.45i) q^{19} +(72.7976 - 803.808i) q^{21} +(-267.753 + 463.762i) q^{23} +(1518.27 + 2629.72i) q^{25} +2784.35 q^{27} +3943.87 q^{29} +(1831.72 + 3172.64i) q^{31} +(-2381.65 + 4125.14i) q^{33} +(1106.67 - 511.942i) q^{35} +(-6319.51 + 10945.7i) q^{37} +(2279.11 + 3947.53i) q^{39} +4814.47 q^{41} +4938.11 q^{43} +(960.499 + 1663.63i) q^{45} +(8702.49 - 15073.2i) q^{47} +(5651.79 + 15828.2i) q^{49} +(1502.18 - 2601.85i) q^{51} +(2329.22 + 4034.32i) q^{53} -7196.30 q^{55} -16292.8 q^{57} +(16250.4 + 28146.6i) q^{59} +(21748.1 - 37668.8i) q^{61} +(-24031.5 + 11116.9i) q^{63} +(-3443.23 + 5963.84i) q^{65} +(-16041.2 - 27784.1i) q^{67} -3333.85 q^{69} -15820.0 q^{71} +(-18257.7 - 31623.3i) q^{73} +(-9452.13 + 16371.6i) q^{75} +(8946.70 - 98786.6i) q^{77} +(12736.1 - 22059.5i) q^{79} +(-16148.3 - 27969.6i) q^{81} -69443.5 q^{83} +4538.91 q^{85} +(12276.5 + 21263.5i) q^{87} +(-54165.4 + 93817.2i) q^{89} +(-77587.5 - 54681.1i) q^{91} +(-11403.6 + 19751.6i) q^{93} +(-12307.4 - 21317.1i) q^{95} +94569.1 q^{97} +156269. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 13 q^{3} - 31 q^{5} + 92 q^{7} - 230 q^{9}+O(q^{10}) \) 10 * q + 13 * q^3 - 31 * q^5 + 92 * q^7 - 230 * q^9	\( 10 q + 13 q^{3} - 31 q^{5} + 92 q^{7} - 230 q^{9} - 351 q^{11} - 108 q^{13} - 1214 q^{15} - 111 q^{17} + 1035 q^{19} - 1365 q^{21} + 3639 q^{23} - 1540 q^{25} - 7214 q^{27} - 1468 q^{29} + 7677 q^{31} + 7439 q^{33} - 19899 q^{35} - 13595 q^{37} - 1406 q^{39} + 10620 q^{41} - 1528 q^{43} - 38978 q^{45} + 6675 q^{47} + 30122 q^{49} + 20975 q^{51} + 30753 q^{53} - 56534 q^{55} - 28778 q^{57} + 87989 q^{59} - 19899 q^{61} - 147318 q^{63} - 119470 q^{65} - 33067 q^{67} + 200798 q^{69} + 217440 q^{71} - 141659 q^{73} + 108788 q^{75} + 271471 q^{77} + 118919 q^{79} + 143851 q^{81} - 422008 q^{83} - 286758 q^{85} + 302154 q^{87} + 55861 q^{89} - 403912 q^{91} - 410381 q^{93} - 26279 q^{95} + 270940 q^{97} + 600308 q^{99}+O(q^{100}) \) 10 * q + 13 * q^3 - 31 * q^5 + 92 * q^7 - 230 * q^9 - 351 * q^11 - 108 * q^13 - 1214 * q^15 - 111 * q^17 + 1035 * q^19 - 1365 * q^21 + 3639 * q^23 - 1540 * q^25 - 7214 * q^27 - 1468 * q^29 + 7677 * q^31 + 7439 * q^33 - 19899 * q^35 - 13595 * q^37 - 1406 * q^39 + 10620 * q^41 - 1528 * q^43 - 38978 * q^45 + 6675 * q^47 + 30122 * q^49 + 20975 * q^51 + 30753 * q^53 - 56534 * q^55 - 28778 * q^57 + 87989 * q^59 - 19899 * q^61 - 147318 * q^63 - 119470 * q^65 - 33067 * q^67 + 200798 * q^69 + 217440 * q^71 - 141659 * q^73 + 108788 * q^75 + 271471 * q^77 + 118919 * q^79 + 143851 * q^81 - 422008 * q^83 - 286758 * q^85 + 302154 * q^87 + 55861 * q^89 - 403912 * q^91 - 410381 * q^93 - 26279 * q^95 + 270940 * q^97 + 600308 * q^99

Introduction

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